# Enhanced Neural Quantum State via Annealed Gradient Descent

arXiv: https://arxiv.org/abs/2607.18865 · HTML: https://mlsanity.com/paper/2607.18865/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions](https://mlsanity.com/paper/2401.10190/) (2024)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Neural network wave functions and the sign problem](https://mlsanity.com/paper/2002.04613/) (2020)
- [Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks](https://mlsanity.com/paper/2105.05650/) (2021)
- [Scalable neural quantum states architecture for quantum chemistry](https://mlsanity.com/paper/2208.05637/) (2022)
- [NNQS-Transformer: an Efficient and Scalable Neural Network Quantum States Approach for Ab initio Quantum Chemistry](https://mlsanity.com/paper/2306.16705/) (2023)
- [Understanding and eliminating spurious modes in variational Monte Carlo using collective variables](https://mlsanity.com/paper/2211.09767/) (2022)
- [A Fully GPU-Accelerated Framework for High-Performance Configuration Interaction Selection with Neural Network Quantum States](https://mlsanity.com/paper/2604.15768/) (2026)

## Abstract (arXiv)

Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional J1-J2 models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.